I heard that a gene mutation can lead to cancers through the change of the base sequence of a gene that codes for certain protein, which are crucial for the regulation of cancer. But I know that chromosome mutations may only change the position of genes in the DNA, not their base sequence (am I correct?) Is chromosome mutation a cause of cancer?

Well, yeah, the chromosome mutations do not cause like short indels, changes in bases etc. But they can cause fusion proteins due to fused chromosome parts. There are some well known examples involved in cancer.

I know chromosome mutations may also result in cancers. For instance, the trisomy, a condition that a person have 3 homologous chromosomes, increase the risk of having leukamia. But what is the principles beneath?

biologyisgreat wrote:chromosome mutations can be deletion, duplication, inversion or translocation

Over-division isn't always caused by altered DNA sequences that code for altered proteins that do not perform their jobs, it can be caused by the same protein being present in different quantities. This can happen if a mutation has caused a gene to appear in the DNA multiple times, or if a gene is moved to another place in the DNA with different controls. Remember that many genes are under specific controls that can respond to aspects of the cell's environment, such as the presence or lack of a chemical compound, by limiting or promoting the translation of certain genes into proteins.